Introduction to PT-Symmetric Extensions of Quantum Mechanics

00:00 03-06-2008

'Courier New'; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: HE">Non-Hermitian Hamiltonians with real spectra arecurrently an active field of research, motivated both by thenecessity to understand their mathematical properties and by therequirement to build a consistent unitary quantum mechanics forthem. A particularly important subset of such operators arenon-Hermitian Hamiltonians which are PT-symmetric, such asH= p^2 + i x^3, or more generally, H = p^2 + x^2(ix)^n with nbeing a real parameter. The reality of the spectrum of theseHamiltonians was discovered about a decade ago by Bender andBoettcher, a discovery which initiated the recent interest andactivity in this field. This talk will be an introduction toPT-symmetric quantum mechanics, to its mathematical structure andto possible applications.